find rate of change of A
#help-0
runic trench
runic trench
silk steeple
Where did you get t from
runic trench
its the instantaneous change of velocity with respect to time
silk steeple
I need some more work on this topic
Do you have any good videos that I can watch that covers this topic
runic trench
do you know what derivatives are
runic trench
dv/dt is the derivative of velocity with time
silk steeple
ohh
The confusing part is the wet area I don’t know what meant
Like how do you calculate that
the book was confusing
runic trench
just sub in
runic trench
thee angle is given, which is 30
v is given 81pi
dv/dt = (what you worked out)
thats another option where the lateral area Al is given in terms of the slant height l
al = pirl = pir*2csc(theta)
so itll be Abcsc(theta)
where the rate of change will be expressed as (dAs/dt)csc(theta)
where theta is given as 30, csc(theta) is 2
then ans will be -4/3
silk steeple
which way is easier?
runic trench
this
runic trench
no
silk steeple
I see
I don’t think I’m ready for this question I need to learn more
that looks like university maths to me 😭
runic trench
idts
runic trench
.close
lone heartBOT
@silk steeple Has your question been resolved?
lone heartBOT
lone heartBOT
Available help channel!
ivory forge
is this a tranitive relation?
lone heartBOT
is this a tranitive relation?
weary wyvern
yes
worn fox
ivory forge
.close
random wagon
Hello;
The task is to make sure no square root is left in the lower part of the fraction. I can't really find anything to start with and so far I have only had dead ends
weary wyvern
Hello;
The task is to make sure no square root is left in the lower part of the ...
try to factor a^3 + b^3
hint: ||treat this as a polynomial in a and use the factor theorem||
edgy flare
You can also multiple the top and bottom by the denominator but use a minus instead of a plus.
Well wait
Yeah
Then you would need to do it again but different exponents
You’ll have something ugly up top
random wagon
try to factor a^3 + b^3
Which would lead to the bottom one being just a+b right? And the top one would be (a+b) * (a+b)^3 or something like that. I'm not too good with roots
novel meteor
@edgy flare it won't work
edgy flare
Why?
weary wyvern
Which would lead to the bottom one being just a+b right? And the top one would b...
no
random wagon
You can also multiple the top and bottom by the denominator but use a minus inst...
I thougt of that. But you have ^1/3 and if I multiply by another it would end up being ^2/3 where I now have to multiply by ^3/2 to get a ^1/1
edgy flare
Ahh
random wagon
Happens
random wagon
3rd Binomial?
edgy flare
the denominator will a^2/3 - b^2/3
Yeah I thought multiplying again with a 2/3 exponent would get rid of it a second time
random wagon
try to factor a^3 + b^3
Are you sure that I can just factor sums?
weary wyvern
yes
random wagon
so it would be a^3 + b^3 / a+b?
This is what I am supposed to get to. And it looks to me a lot like the 2nd binomial except for the middle part
dawn comet
need help asap w/ sollution if possible thanks
lone heartBOT
need help asap w/ sollution if possible thanks
normal holly
oh shoot
lone heartBOT
@dawn comet Has your question been resolved?
real lance
hi i need help with this question
lone heartBOT
hi i need help with this question
real lance
this is my work so far
im just not sure about how to get the solution set or the answer at this point
real lance
something like S = {x ∈R|
but im confused how to get it
i am not sure how to tell which lines are correct from the table based off the question
ornate condor
table?
real lance
here
tall topaz
You should make a number line with the critical values.
real lance
You should make a number line with the critical values.
how can i know my number line is correct
tall topaz
Draw a number line with the two critical values
Then see what happens the the thing inside the absolute value in each part of the number line
If it’s negative then flip the sign (times by -1)
real lance
how can i know from my table which lines are supposed to be included in the solution set?
tall topaz
Why don’t you draw a number line first
real lance
okay i will try
tall topaz
It’s much easier than a table
real lance
then what should i do after?
tall topaz
Consider what happens when x is less than -1/4
(To the left of the number line)
$|4x+1| - |2x-3| \geq 0$
ocean sealBOT
Pure
tall topaz
Consider the 4x+1 and 2x-3 in that region
If it’s negative then the modulus means you times it by -1
thick lynx
ocean sealBOT
Kepe
keen plinth
thats exactly how a geomtric series works
look it up
its taught some places in highschool
at least where im from
finite geometric series are definitely doable for highschool
neat frost
I worked on this question for a while and I have a few questions. It's due today
neat frost
It might be kind of a simple one from herstein but I've looked at solutions and I don't understand them. It's the one that says G is a finite abelian group in which the number of solutions in G of the equation x^n = e is at most n for every positive integer n. Prove that G must be a cyclic grou
group
I think I have to find the largest k such that some g in G has g^k = e. For the sake of contradiction, show that there is an h in G that's not in <g> by showing 0(h) |o(g) so there exists some g^j in <g> with the same order as h which will somehow contradict x^n = e has at most n integer solutions
I don't really know how to construct this proof though. This is the last question on the homework I just can't figure out
lone heartBOT
@neat frost Has your question been resolved?
mortal trellis
what have you tried to prove these things? what do the solutions say that you have read?
lone heartBOT
@neat frost Has your question been resolved?
tawdry stirrup
Hi, is there anyone who know how to solve it?
lone heartBOT
Hi, is there anyone who know how to solve it?
normal junco
U gotta try to simplify the expression
Why not put the $(x-1)$ inside the small square root?
ocean sealBOT
dmbd
normal junco
And try to solve it from there
neon scarab
Hi, is there anyone who know how to solve it?
Hint: Keep squaring until you make gone all the radicals, then start simplify.
normal junco
yep just saw that
neon scarab
Another hint: You may want to reject some solutions at last.
slow hound
,w 3135 factorization
alpine sable
Hi, i was wondering how I would go about doing this transformation?
normal junco
the figure hasn't change
so it is a translation
start by thinking how can you keep it's form
(I'm assuming the objective is the red one)
alpine sable
Well i know i should shift the solid black function down 5, and to the right by 3, i guess i’m mostly confused on how i would write that
normal junco
ok let's go by parts
first horizontaly
imagine instead of f(...) you only have y
$2y-3$
ocean sealBOT
dmbd
alpine sable
why would we change it?
normal junco
you wont
is just to tell you that when you change things outside y, you changing it horizontaly
like when you sum (or subtract something) you're moving it by that many distance
alpine sable
do you mind if i close this channel, i kinda want to sit and work on this for a bit?
normal junco
go ahead
alpine sable
lone heartBOT
alpine sable
One pigeon sat on the roof of the house and on the lantern. Anniša spilled grain near the house. Both pigeons took off at the same time and, flying at the same speed, reached the grain at the same time. Calculate how far from the house Anniņa spilled the grain, if you know that the house is 10 m and the lantern is 4 m high. The lantern is 10 m away from the house. The grain is m from the house (Enter the exact value!) Tip: the required distance is denoted by x!
i don’t know how to move on
<@&286206848099549185>
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
Plz help this is really important
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
<@&286206848099549185>
carmine reef
how far is the grain from each pigeon if it is x meters away from the house
alpine sable
I have no clue
carmine reef
use pythagorean theorem
alpine sable
.close
past socket
f(x) = x^3 - 3x^2 - 9x + 27
I know that I need to factor this polynomial, and I know how to factor by grouping, but how would I factor with X-Factor? My professor taught me a week ago but I don't remember and can't figure it out by looking at past work.
echo socket
What's X-Factor?
past socket
Drawing an x and putting in the values to find out the factored answer
echo socket
Ah, I think I've seen that, isn't it for quadratics though?
past socket
ive seen it used on trinomials
echo socket
idk then
past socket
ok, then if I were to normally factor, like factoring by grouping
would the answer of x^2(x-3)-(x+9)(x+3) be correct?
past socket
why would it be -9x(x-3)
echo socket
Ah mb, just 9
past socket
why would it be 9(x-3)
echo socket
Because -9(x - 3) = -9x + 27
past socket
so because the common factor between -9x and 27 is -9, I'd factor that out of the parentheses?
echo socket
Yeah
echo socket
ok so if I have x^2(x-3)-9(x+3)
- 9(x - 3)*
echo socket
would that be enough to find the y-intercept?
You can find the y-intercept without factoring anything
past socket
ok i dont understand
echo socket
Do you want to factor the polynomial or find y-intercept?
past socket
both
weary wyvern
What's X-Factor?
Pretty sure that's a singing show
past socket
I need to state the zeros, their multiplicity, find the y-intercept, end behavior, and sketch a graph
all things i will use in real life but yeah
i dont know how to do this
past socket
what does factoring even mean
echo socket
So x^2(x - 3) - 9(x - 3), can you see the next step?
echo socket
what does factoring even mean
Putting stuff out of parenthesis basically
past socket
the next step would be to divide the x-3 out of both sides, right?
echo socket
Opposite of expanding the parenthesis
past socket
so it'd be x^2-9?
echo socket
Yeah, (x - 3)(x^2 - 9)
You can also rewrite x^2 - 9 as (x - 3)(x + 3), because a^2 - b^2 = (a - b)(a + b)
echo socket
Okay look ax^2 - 9a = a(x^2 - 9), right?
echo socket
Just an example to make sure that we're on the same page
past socket
were not
echo socket
Okay look ax^2 - 9a = a(x^2 - 9), right?
Yes or no?
past socket
no
echo socket
Are you sure you know what factoring is?
past socket
yeah
echo socket
And how it's done
past socket
well no
echo socket
ab - ac = a(b - c), right?
Then you should be able to agree with this
past socket
thats why im asking for help on how to factor
if I knew how to then I wouldn't be asking how to
echo socket
ab - ac = a(b - c), right?
Sure, but this is an elemental example of factoring, idk why you're disagreeing with this
past socket
never heard of that equation
^
alpine sable
lone heartBOT
alpine sable
How would I begin to actually write a proper proof for this?
I thought that this would be what is considered to be a proof
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
.close
alpine sable
I have an issue that has been giving me a bit of trouble. We are dealing with Vertex Form and Parabolas. I've split the equation into 4(x^2-x)-21 from 4x^2-4x+21 and I am confused on how x^2-x is factored in this scenario. The final Vertex is (1/2, 20) but I am stumped on the steps to get there.
hearty citrus
$4(x^{2}-x)-21$
ocean sealBOT
Krispeh
hearty citrus
ah ok
hearty citrus
It's supposed to be +21
and then
you ignore the 4 outside the brakets and just complete the square with the $x^2-x$ part
ocean sealBOT
Krispeh
hearty citrus
you should get $(x-1)^{2}-1$
ocean sealBOT
Krispeh
hearty citrus
or fully $4((x-1)^{2}-1)+21$
ocean sealBOT
Krispeh
hearty citrus
now you can add the constants at the end and divide by 4
and use vertex equation to finish it off
hearty citrus
I have an issue that has been giving me a bit of trouble. We are dealing with Ve...
$v=-\frac{b}{2a}$
ocean sealBOT
Krispeh
alpine sable
i need to find the area
(x+4)^2+(x+9)^2=4
did i get this right? pi x 4^2
minor needle
i need to find the area
(x+4)^2+(x+9)^2=4
did i get this right? pi x 4^2
nope, r = 2, so it's 4pi
alpine sable
nope, r = 2, so it's 4pi
4 times pi?
minor needle
ye
alpine sable
ok ok
minor needle
,calc 4pi
ocean sealBOT
Result:
12.566370614359
Well you said 25.01
Output says 25.10
Maybe that's it
But the problem just says to the nearest second
So probably you should've said 25
dense nova
lone heartBOT
dense nova
not sure what the answer for this might be, i tried setting the demoniator to zero but im completely stuck
minor needle
not sure what the answer for this might be, i tried setting the demoniator to ze...
$$1-e^{x^2-5}=0$$
$$e^{x^2-5}=1$$
$$x^{2}-5=\ln 1$$
$$x^{2}-5=0$$
Maybe now?
ocean sealBOT
Modus
lone heartBOT
@dense nova Has your question been resolved?
fathom halo
lone heartBOT
fathom halo
I don't understand this at all
stoic cliff
Do you know what the general equation of a line is?
fathom halo
no
stoic cliff
So you’ve never heard of y = ax + b ?
fathom halo
oh i heard of that
stoic cliff
Do you know what a and b are
stoic cliff
Match Graph/Equation Ax + By = C (MC)
idk what u mean by this
coral moss
you can change that into y = mx + c (or ax+b whatever it's called) and then compare every graph to what you have
fathom halo
uh
coral moss
for example if m is negative then you can get rid of graph A as a potential answer since that shows a positive gradient
coral moss
good idea to first note down all the facts you're given. For this:
gradient is positive (you can work it out if it helps)
y intercept is 18
x intercept is -12
then use that to find an answer
fathom halo
k thx
lone heartBOT
@fathom halo Has your question been resolved?
hoary flare
Would -3 be divergent?
lone heartBOT
Would -3 be divergent?
hoary flare
.close
fathom halo
10x−8y=32?
lone heartBOT
10x−8y=32?
fathom halo
What is that graphed
tacit arch
,w plot 10x - 8y = 32
ocean sealBOT
fathom halo
ohhh thx
tacit arch
wolframalpha is your friend
alpine sable
But also if you're supposed to graph it physically try using algebra to get it in slope-intercept form to make it easier to graph. Also, digitally I recommend desmos.com/calculator for graphing if you dont want to post it to a Discord bot every time.
tacit arch
true true
lone heartBOT
@fathom halo Has your question been resolved?
foggy knot
lone heartBOT
foggy knot
any helperz?
wise thistle
any workz?
foggy knot
rip
wise thistle
lmao soz dude
autumn pasture
hellooo!
for your 7xy, you can use product rule
but when you differentiate y you need to multiply by dy/dx
rose inlet
What's ∞/-∞
lone heartBOT
What's ∞/-∞
rose sigil
what's ∞? what's /? what's -∞?
native cloud
Undefined
worthy badger
lone heartBOT
worthy badger
Wasn't in class today so im kinda stuck on some parts
alpine sable
what this is asking is basically
for what value of radians is the cosine = sqrt(3)/2
worthy badger
ye
alpine sable
do you know the unit circle
worthy badger
Ya... here ill explain what ik so far for this problem
alpine sable
sure
worthy badger
So pretty much cos is about the x value... so i have to find the x value for that equation on the unit circle. Now there are multiple sqrt 3/2 x values on the unit circle... ik that there are some restrictions to help u narrow down which one it is by figuring out which quadrants it could be in. in this case since cos is positive it could be in quadrant 1 or 4... my problem is how to figure out which one it is when there's still mutliple options left after narrowing it down
alpine sable
the restrictions for cos^-1 / arccos (inverse cosine)
is 0 to pi
meaning the top half of the graph
worthy badger
ohh
worthy badger
alr
but what if u still have multiple options?
ill probably encounter a problem like that later on
worthy badger
oh ok
alpine sable
you will notice the restrictions have one quadrant with positive value and one for negative
worthy badger
broo that's a good image
ngl all the numbers on the bottom make it confusing
but the picture helps
alpine sable
ya for the mumbo < x < jumbo
just remeber that one full rotation is 2pi
and one half rotation is pi
and one half of that is pi / 2
worthy badger
ye
alr bro i appreciate the help!
@alpine sable alr so I went through 5 of the problems with no problems bc it was sin or cos
But now since it’s tan I’m kinda confused @alpine sable
bc it's y/x
worthy badger
yes
worthy badger
that idk
worthy badger
we don't need to memorize it.. yes i have one in front of me
alpine sable
ok look at the first quadrant
worthy badger
yes
alpine sable
well theres only three possible values and the rest of the unit circle is variations with positive/negative
you can probably memorize it by just doing a lot of problems
worthy badger
well theres only three possible values and the rest of the unit circle is variat...
i better guess right then
in terms of choosing which one to divide first
alpine sable
(1/2)/(sqrt(3)/2)) is not that long
worthy badger
ah ok so it's pi/6
@alpine sable
I tried the method for this problem and it says I’m wrong…
alpine sable
<@456226577798135808>
try -pi/3
alpine sable
its the sMe thing as 5pi/3
when you say negative it just means your rotating in the opposire direction
alpine sable
negative radiabs means it is rotating clockwise
and positive radians is counter clockwise
worthy badger
why wouldnt it just be -5pi/3 then
worthy badger
thats = pi/3 lol
how u simplify the 5 tho
worthy badger
search up a vid with visuals it will help you visualize
alr
patent bluff
lone heartBOT
lone heartBOT
@patent bluff Has your question been resolved?
deep grove
o/
what part do you need help with
what have u tried
ok have u found the equation for y
ok so with this, u can sketch the graph right?
use the points in the table
and plot those
alpine sable
lone heartBOT
ornate condor
draw a diagram
alpine sable
I DID
ornate condor
hows it like
alpine sable
MY TEACHER DOESNT TEACH THE CONCEPTS BUT ASKS THE QUESTIONS
I dont know what to do that’s why I’m asking here
If I knew, I wouldn’t be asking here, would I ?
I drew a diagram and it’s non sensical and I’m not getting the correct answer
IT SHOULD BE GIVING ME THE CORRECT ANSWER WHEN I USE PYTHAGOREAN THEOREM! BUT IT DOES NOT!
IT SAYS THE CORRECT ANSWER IS 19.56 OR SOMETHING!
AND WHEN I ASK FOR HELP HERE I AM DISREGARDED!
: (
swift shore
@alpine sable can you send the diagram you drew
alpine sable
a circle with a cartesian plane in it
swift shore
well there's more than that, like the radius and angle and whatnot
alpine sable
i did
alpine sable
I can draw one now
alpine sable
Since I am away from my workspace
I apologize for this low effort diagram, I am away from my workspace at the moment
swift shore
ah this is why
so
the whole ferris wheel is 11 m above the ground
in other words, the bottom of the circle should be 11 units above the ground
alpine sable
I have no idea how to implement a circle into this , I am so sorry
Okay so it should be something like this ?
@swift shore
alpine sable
Yes
swift shore
cool
alpine sable
How do I find the height !
swift shore
the ? is what they're asking for; i.e. carl's height above the ground
that's a great question
so let's notice a couple things
alpine sable
Do I find the hypotenuse with cosine and 72 degrees ?
swift shore
well you're on the right track, we will be doing trigonometry
but we already know the hypotenuse
what is it?
swift shore
nice
yeah so no matter where carl is, the ferris wheel is always 11 m above the ground
so it's gonna be (something) + 11
how about we find the height of carl above the centerline of the circle?
how would you do that?
alpine sable
sin(72)x9?
alpine sable
19.6 (rounded to the nearest tenth)
Thank you my friend, I now know what to do. Thank you so much
swift shore
wait hold up lemme check that
alpine sable
Ok
swift shore
how did you get 19.6
alpine sable
Sin(72)x9 = 8.559
swift shore
look back at this; you have 11 + (something) + 8.559
alpine sable
The answer says its 19.56
swift shore
what? really?
alpine sable
Yes
swift shore
oh I'm so stupid...
it said the center of the wheel is 11 m above the ground
not the bottom...
alpine sable
No you aren’t, dont worry. Everyone makes mistakes
I am better with quadratics and radicals than this, this is very hard for me because I have to imagine it, I am not a creative person lol : (
alpine sable
I am so grateful for your help
alpine sable
Have a good day/night!
No thank you, I solved one of the problems I was also struggling with
Thanks again
swift shore
ah nice
alpine sable
.close
lone heartBOT
lone heartBOT
Available help channel!
cedar field
The problem:
$xe^{-x}$.
1.differentiate x integrate $e^{-x}$.
2.derivative of x is 1 , integral of $e^{-x}$ is $-e^{-x}$.
3.the product of that is $-e^{-x}$ and the integral of the product is $-e^{-x}$.
if we plug all this into the formula it is $1 (-e^{-x}) - (-e^{-x})$.
that simplified is $e^{-2x}$.
khan academy says it is $-e^{-x}(x+1)$. so please find what I did wrong?
ocean sealBOT
kangaroo rat
ocean sealBOT
jan Niku
alpine sable
**jan Niku**
u missed the v in integral of u dv
cedar field
@remote heron I think I use a different way from you...
remote heron
i missed the v 
alpine sable
oh nvm
runic trench
let u = x dv=e^-x
remote heron
yea
alpine sable
my brain kinda died there
remote heron
youve just made a mistake maybe from not keeping track of intermediate results
but just eyeball what you expect out
you have an exponential as dv
and a x as u
so just super super super roughly eyeballing
youd expect the integral to evaluate to something like xe^x-e^x
just a guess
which makes sense
since this looks like e^x(x-1)
so pretty close in form
runic trench
runic trench
lmao
cedar field
So did I just make up a whole strategy lol
cedar field
can you please teach it to me?
alpine sable
$\int xe^{-x} dx$
$\int e^{-x} dx=-e^{-x}+C$
as we care about any 1 solution[as for reversing product rule we let C=0 sometimes in IBP u can get some nice tricks by letting C be something else]
$=-xe^{-x}-\int -e^{-x} dx$
$=-xe^{-x}-e^{-x}+C$
ocean sealBOT
cardioid
cedar field
$\int xe^{-x} dx$
$\int e^{-x} dx=-e^{-x}+C$
as we care about any 1 solution...
do you have to define C?
alpine sable
C is constant of integration
when u differentiate something the constant term doesn't matter
cedar field
and could someone please try teach me integration by parts?
alpine sable
so we take in consideration the general form of the anti derivative
alpine sable
and could someone please try teach me integration by parts?
ok
cedar field
thanks
alpine sable
consider u have $\int f'(x)g(x)+f(x)g'(x)dx$
ocean sealBOT
cardioid
cedar field
yup
alpine sable
**cardioid**
do you manage to get an answer?
cedar field
do you manage to get an answer?
no...
alpine sable
you know product rule in derivatives?
cedar field
you know product rule in derivatives?
I havent practiced those rules in a while
alpine sable
I will reccomend u revise ur derivatives very well before going into integration
cedar field
its only the rules
runic trench
ok find derivative of xcosx @cedar field
cedar field
do you think I should go deep into the rules or just quickly learn how to use them?
cedar field
ok find derivative of xcosx <@953140475693514804>
xcos(x) =-x sin(x)
runic trench
show steps
runic trench
differentiate using the product rule
runic trench
differentiate using the product rule
Telling u to use this so we can know if u know how to apply product rule
cedar field
Telling u to use this so we can know if u know how to apply product rule
i cant
idk it
runic trench
Ok then u have to read up on product rule
cedar field
Ok then u have to read up on product rule
ok
cedar field
do you think I should go deep into the rules or just quickly learn how to use th...
so what about this?
@runic trench
eternal ocean
I've tried three different ways to figure out the answer for this limit
the answer key in the book says that its -1/2 which is what I got in the 3rd try
but I don't get it still and I'm not sure if I even did it correctly
tacit arch
why are you just multiplying by x+1 here?
eternal ocean
oh wait do I need to make it (x+1)/(x+1)?
I multiplied it thinking that it'd make the denominators the same
tacit arch
oh wait do I need to make it (x+1)/(x+1)?
I multiplied it thinking that it'd mak...
yes you have to multiply it by 1
otherwise you're changing the problem
$\frac{x+1}{x+1} = 1$
ocean sealBOT
riemann (eric tao for honorable)
eternal ocean
oooo will that fix the whole thing then?
tacit arch
maybe.
eternal ocean
ok ill try it
im going in the same loop again and im convinced I’m multiplying it wrong but I don’t where
tacit arch
simplify the top and stuff should cancel
eternal ocean
tacit arch
nah that's not how algebra works
lone heartBOT
@eternal ocean Has your question been resolved?
tacit arch
would it be (x-1)/(-x+1)(x+1)
yes. now factor -1 and then cancel
eternal ocean
BRUH it was the factor the whole time? I really sat here and redid this 5x over
thanks
.close
dark fog
is b = 7?
tacit arch
• Show your work, and if possible, explain where you are stuck.
lone heartBOT
@dark fog Has your question been resolved?
tacit arch
so i plugged 2 into x for x^2 -3=3x+b
This is correct
But I don't get how you got b=7 from that
Probably just algebra mistakes
dark fog
i did negative n for the first x
wait
is it supposed to be the otherway around
2^2-3 =3^-2 +b?
tacit arch
i did negative n for the first x
Why negative
dark fog
the limit?
dark fog
or am i reading the limit wrong
tacit arch
It's just 2
tacit bobcat
so negative 5?
yes
tacit bobcat
so for when b is -5 x = 2
I don't know how to read this, but b = -5 fits continuity
dark fog
"for what value of b is f(x) continuous at x=2"
tacit arch
This channel's occupied. Read #❓how-to-get-help
dark fog
.close
royal cloak
is there any rule in inequality that when -ve values are squared both side then the sign changes?
royal cloak
or raised to any +ve power
slender gull
-2 < -1
If you want to square both sides, you get 4 < 1
Which is not true, so I suppose you could, if you wish to, remember that and change the sign.
But it's always better the square the sides only when you have both sides of the same sign and that too preferably postive.
slender gull
What is?
royal cloak
chabging the sign
royal cloak
with -ve values both side
slender gull
if both sides are < 0, flip the sign after squaring, yes.
royal cloak
mmm
vale wigeon
the function x ↦ x^2 is decreasing on (-∞, 0]
lone heartBOT
@royal cloak Has your question been resolved?
dire juniper
how do i solve this
lone heartBOT
how do i solve this
lone heartBOT
@dire juniper Has your question been resolved?
turbid kestrel
How would I solve this?
lone heartBOT
How would I solve this?
turbid kestrel
gray isle
start with their instructions
turbid kestrel
I tried setting u as x^2+4 but I cant figure out how to get rid of the 2x^3
gray isle
did you go through the standard steps of substitution
turbid kestrel
yes
gray isle
what do you have right now
gray isle
not that from the sub u = x^2 + 4
x^2 can be expressed in terms of u
u = x^2 + 4 → x^2 = ?
turbid kestrel
u-4?
gray isle
yerh
turbid kestrel
ok thank you!!
sudden lodge
can someone help
lone heartBOT
can someone help
sudden lodge
with linear expression
trim wagon
trim wagon
Where’s the question
gray isle
Where’s the question
sudden lodge
BRUH
trim wagon
If you want, Khan Academy is good resource to learn
sudden lodge
thanks
sudden lodge
If you want, Khan Academy is good resource to learn
thanks
trim wagon
Sure np 
lone heartBOT
@sudden lodge Has your question been resolved?
scenic wedge
lone heartBOT
alpine sable
ooooooh
that looks fun
use algebra
and balance the equation
and bam
your done
alpine sable
algebra
is godly
is all it means
balance the equation with the variables
and find the rule
a good way to do this
is to graph it or do a table of values
scenic wedge
lone heartBOT
@scenic wedge Has your question been resolved?
alpine sable
what have you done?
Probability of choosing exactly two even numbers = 5C2 because you choose 2 even numbers from a set of 5 elements {2,4,6,8,10}
Probability of choosing exactly two odd numbers = 5C2 because you choose 2 odd numbers from a set of 5 elements {1,3,5,7,9}
Now it's just a matter of using the hypergeometric distribution as you've posted with the denominator being something like 10C4 since you're choose 4 elements from a set containing 10
plucky geyser
Can I use the integrating factor here?
lone heartBOT
Can I use the integrating factor here?
vale wigeon
if you find something that serves the role of an integrating factor, then by all means go for it.
ancient meteor
Yes
plucky geyser
*runs away*
Don't run away, it loves you!
alpine sable
You should love ODE's at least
ordinary differential equations ? what a sick joke
plucky geyser
yeah it is
alpine sable
no differential equation is ordinary
vale wigeon
plucky geyser
Can I use the integrating factor here?
is that too?
vale wigeon
anyway yeah your work checks out
lone heartBOT
lone heartBOT
Available help channel!
tender magnet
lone heartBOT
tender magnet
can someone help me with understanding two dimensional kinematics?
currently i only understand where we have to separate the x and y component to find different values like time of flight and displacement.
lone heartBOT
@tender magnet Has your question been resolved?
frail trail
If we neglect air resistance it's (b) otherwise it's (d)
This is the case because gravity acts downwards and at the peak the projectile only has a horizontal component
tender magnet
oh i see
mind explaining to me how does the velocity vector becomes horizontal ?
oh wait, is the velocity the hypotenuse of the vector triangle? if so it'll make sense
frail trail
oh wait, is the velocity the hypotenuse of the vector triangle? if so it'll make...
Yes
tender magnet
but where does the x component go if thats the case?
tender magnet
oh i mixed them up i suppose
frail trail
Not that it matters you can define x to be up if you want but it's not typical
tender magnet
is the a the y component? because thats what i thought of it jn
or is the a and v not the same thing
frail trail
a is the acceleration
limpid spade
^
frail trail
v is the velocity
frail trail
a and v are vectors. They individually have x and y components so it doesnt make sense for a to be the y component
frail trail
Yes since its a vector
tender magnet
what else could be a vector other than velocity and acceleration? or its just that two
limpid spade
Lots of things
frail trail
In what context?
tender magnet
kinematics
frail trail
You have jerk
tender magnet
projectile motion
frail trail
And then the derivative of jerk
tender magnet
its hard to make sense of it
limpid spade
pop
frail trail
Potentially infinite derivatives of your velocity vector
frail trail
Briefly it's a way of saying how a function changes with respect to an increase in its inputs
So for kinematics if you increase the time then how has your velocity changed
That's what the derivative tells you
tender magnet
does it have its own formula? im not sure if this is one but ill type it out
dx/dt
frail trail
dx/dt means how does x change when we change t
tender magnet
whenever i see this i dont know what to do
tender magnet
dx/dt means how does x change when we change t
still dont understand that well enough
frail trail
You can think of d as meaning delta which is the first letter of a Greek word meaning "difference"
frail trail
Yes its delta x / delta t
Dont get confused and think that d is it's own symbol because it isn't
tender magnet
so its basically the normal formula for finding velocity?
frail trail
I.e. You can't cancel them out
tender magnet
oh
frail trail
For vectors dx/dt would tell you the velocity of the x component yes
And then you would find dy/dt and then you'd have a velocity vector
tender magnet
so this could only be used in finding components and vectors?
frail trail
Derivarives?
tender magnet
yes
frail trail
No it's an integral part of mathematics
You find it everywhere
And everywhere in physics too of course
frail trail
I can either explain derivatives to you or I can recommend and amazing video which will explain it 100x better than I ever could?
I'm happy for you to come back and ask me questions after you've watched the video anyway
tender magnet
oh yeah sure, ill do that
frail trail
oh yeah sure, ill do that
https://youtu.be/9vKqVkMQHKk it's a bit long but I would easily say it's worth it. You might even want to watch the first video in the series because you'll need to probably learn integrals too
Just lmk if you dont understand something
frail trail
ill get back to you if i have other questions
Cool beans
lone heartBOT
@tender magnet Has your question been resolved?
hollow elm
hello
frail trail
i dont know if fg(x) means f(x)*g(x) or f(g(x))
Pretty sure it's the latter; composition
nimble aspen
Design and implement the function void inclusion (double eps, double v) that approximates √v
through a sequence of pairs of values (a0, b0),(a1, b1), . . . ,(an, bn) having the property:
ai · ai ≤ v and bi · bi ≥ v
The value of a0 is 0. The value of b0 is the maximum of v and 1.
nimble aspen
i have this assignment but i have no clue what: "The value of b0 is the maximum of v and 1 means"
gilded citrus
b0 = max(v, 1)
nimble aspen
what does that do
gilded citrus
picks whichever is larger
wet beacon
Hi guys, how do I prove 2^a+1=x^2 for a and x are positive integers only have 1 solution?
valid lake
yes?
wet beacon
How do I prove the only method
valid lake
u know what;s 2^0 ?
wet beacon
1
valid lake
yes
wet beacon
My TEAHCER only let me use grade 8 method
He said I wouldn’t be able to use graphs / Calc in exam
valid lake
$2^a + 1 = x^2$
ocean sealBOT
Mystery Man
valid lake
is it this ?
wet beacon
I know, answer can be a=0 and x=1
wet beacon
is it this ?
Yes
valid lake
it's positive too and negative too
wet beacon
Yes
But he said both need to be positive
And I figured it out 3 and 3 is the only answer
And he told me to prove it
Does anyone know??
little drum
$2^a = (x^2 - 1) = (x + 1)(x - 1)$
ocean sealBOT
Arya
little drum
For 2 to divide the right hand side, x must be of the form (2k + 1). Therefore, $$2^a = 4k(k+1)$$
ocean sealBOT
Arya
wet beacon
Hmm
little drum
or \ $2^{a-2} = k(k+1)$
ocean sealBOT
Arya
little drum
the right hand side can only be even for k = 1, and hence you have your one and only solution
wet beacon
Ohhhhh
TYSM
Wait,
What about other values
Like 3,5,7… they’re odd numbers but they will be even
Hello @little drum ?
lone heartBOT
@wet beacon Has your question been resolved?
lone heartBOT
@wet beacon Has your question been resolved?
ornate condor
$2^a=x^2-1$
ocean sealBOT
